Edit mode Toggle and select faces in one shortcut. How possible is it?
To perform two steps from one shortcut, you will need to make your own operator, by putting it into your own addon you can make it active every time you start blender.

Combining two existing steps is simple, you just need to call both existing operators from yours. You can then add a shortcut by using the bl_idname from the operator in the input settings.

To be able to cycle through the selection modes, you look at what the current mode is.

bl_info = {
    "name": "Edit mode with face select", "author": "sambler",
    "version": (1, 0), "blender": (2, 75, 0),
    "location": "blender", "category": "Object",
    "description": "Enter edit mode and set selection type to face.",
    }

import bpy

class EditSelectOperator(bpy.types.Operator):
    bl_idname = 'object.edit_face_select'
    bl_label = 'Enter edit mode and set face selection.'

    def execute(self, context):
        if context.object.mode != 'EDIT':
            # if we aren't in edit mode goto edit and set face select
            bpy.ops.object.mode_set(mode='EDIT', toggle=False)
            bpy.ops.mesh.select_mode(type='FACE')
        else:
            # if we are editing cycle through selection modes
            sel_mode = context.tool_settings.mesh_select_mode
            if sel_mode[0]: # vertex
                bpy.ops.mesh.select_mode(type='EDGE')
            elif sel_mode[1]: # edge
                bpy.ops.mesh.select_mode(type='FACE')
            else: # face
                bpy.ops.mesh.select_mode(type='VERT')
        return {'FINISHED'}


def register():
    bpy.utils.register_class(EditSelectOperator)

def unregister():
    bpy.utils.unregister_class(EditSelectOperator)

if __name__ == "__main__":
    register()